Spherically Symmetric Vacuum Brane and Wormhole Solutions

In this letter, we have obtained static, spherically symmetric solutions of the effective vacuum Einstein field equations on a brane embedded in a five dimensional space time. The effective stress tensor is induced by the interaction with the bulk gravitational field and is given by the electric part of the five dimensional Weyl tensor. Due to traceless nature of this non-local effect of the bulk, any solution of  ⁽⁴⁾ R=0 is a possible solution of the vacuum brane. We have derived a class of solutions, which corresponds to wormhole solution. Physical properties and characteristics of the wormhole are studied.     

Gravitational collapse and higher-order gravitational lagrangians

A general form of higher-order contributions (in R_ij) to the Einstein field equations is displayed. The additional terms may either stabilize or destabilize self-gravitating objects in gravitational collapse depending on the sign of the coefficient introducing the quadratic term. If the quadratic term is stabilizing, intertial mass can be converted to radiation with an efficiency approaching 100%, and arbitrarily large masses can be stabilized. On the other hand, the resultant field equations are pathological in that they admit gravitons with negative mass-squared (i.e., tachyons). A nonsingular class of vacuum solutions exist in general for the quadratic case (“grey dimples”).     

Exact wave solutions of the five-dimensional einstein equations

Exact wave solutions are found for the five-dimensional Einstein equations in a vacuum. The solutions describe the consistent gravitational scalar wave processes [6] and generalize to five dimensions the known four-dimensional Einstein-Rosen and Bondi-Pirani-Robinson wave metrics and the Rosen metric. By means of the method of rotations involving the coordinates of x⁵, the solutions obtained are generalized to the case in which there is an electromagnetic field present. For each of the solutions, the three-dimensional electric and magnetic field strengths are found. Moscow University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 112–117, October, 1996.     

Global Foliations of Vacuum Spacetimes withT2Isometry

We prove a global existence theorem (with respect to a geometrically defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit aT²isometry group with two-dimensional spacelike orbits, acting onT³spacelike surfaces.     

Exact solutions of the Bach field equations of general relativity

Conformally invariant gravitational field equations on the hand and fourth order field equations on the other were discussed in the early history of general relativity (Weyl Einstein, Bach et al.) and have recently gained some new interest (Deser, P. Günther, Treder, et al.). The equations B_αβ=0 or B_αβ=?T_αβ, where B_αβ denotes the Bach tensor and T_αβ a suitable energy-momentum tensor, possess both the mentioned properties. We construct exact solutions ds²=g_αβdx^αdx^β of the Bach equations: (2, 2)-decomposable, centrally symmetric and pp-wave solutions. The gravitational field g_αβ is coupled by B_αβ=?T_αβ to an electromagnetic field F_αβ=?F_αβ obeying the Maxwell equations or to a neutrino field ?A obeying the Weyl equations respectively. Among interesting new metrics ds² there appear some physically well-known ones, such as the De Sitter universe, the Weyl-Trefftz metric. and the plane-fronted gravitational waves with parallel rays (pp-waves) known from Einstein's theory. The solutions are built up by means of special techniques: A separation method for (2, 2)-decomposable solutions, simplification of centrally symmetric metrics by a suitable conformal transformation, and complex function methods for pp-wave solutions.     

Common solutions of the einstein and Brans-Dicke theories

It is shown that non-trivial solutions common to the vacuum field equations of the Einstein and of the Brans-Dicke theories necessarily representpp-waves and the set of all common solutions is precisely the set of allpp-wave solutions of the Einstein equations. The form of the associated scalar field is found and is shown to be singular when ω相似文献   

The harmonic-map structure of the axially symmetric stationary Einstein equations

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH ₁ ² with a totally geodesic map fromH ₁ ² into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.     

Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves

We construct a class of exact solutions of the noncommutative Einstein field equations in the vacuum, which are noncommutative analogues of the plane-fronted gravitational waves in classical gravity.     

A family of Jordan-Brans-Dicke Kerr solutions

A family of solutions of the vacuum Jordan-Brans-Dicke or scalar-tensor gravitational field equations is given. This family reduces to the Kerr rotating solution of the vacuum Einstein equations when the scalar field is constant. The family does not have spherical symmetry when the rotation is zero and the scalar field is not constant. The method used to generate the new solutions can also be used to obtain vacuum Jordan-Brans-Dicke solutions from any given vacuum stationary, axisymmetric solution.     

Detection of spin excitation transfer in a two-dimensional electron system via photoluminescence of multiparticle exciton complexes

A modified-gravity theory with a four-form field strength F, a variable gravitational coupling parameter G(F), and a standard matter action are considered here. Maxwell and Einstein equations are now derived when including to action also derivates of F. The energy momentum tensor of the 4-form field contains both the part, which is typical for the fundamental (pseudo)scalar, and the part, which cancels the divergent contribution of the zero-point energies of quantum fields to the vacuum energy and thus leads to the natural nullification of the cosmological constant in Minkowski vacuum.     

Colliding gravitational waves with noncollinear polarization: A class of soliton solutions

We construct a general class of exact solutions of the vacuum Einstein field equations describing the interaction of colliding gravitational plane waves with noncollinear polarization by using the inverse scattering method.     

Linearization procedure for cylindrically and axially symmetric space-times

An investigation of the vacuum Einstein gravitational field equations for cylindrically and axially symmetric space-times is presented which leads to an equivalent differential system involving a simple nonlinearity only. The case when this equivalent system is linear is analyzed in detail and two methods for generating solutions of the Einstein vacuum equations are set up. As a result, in the axially symmetric case the linearity of the equivalent system characterizes completely the Kramer-Neugebauer transforms of Papapetrou line elements. Accordingly, Weyl solutions are shown to generate exhaustively both Lewis and van Stockum solutions. Analogous results are obtained also in the cylindrically symmetric case.     

On the analogy between the plane and the spherical solutions of einstein equations in the vacuum

It is shown that some simple and interesting analogy between the plane and the spherical solutions of Einstein gravitational equations in vacuum exists. This analogy is applied to the solutions of some problems of motions in the plane gravitational field.The authors thank I. Kraval for performing some calculations.     

Solution of the Einstein-Maxwell equations for a static distribution of massive charged particles

Exact solutions of the general relativistic field equations of Einstein and Maxwell have been found for a general static distribution of massive charged particles. As in the Newtonian case, the particles must have unit charge to mass ratioe ²/m ²=1. The active gravitational mass of the system of particles is precisely the sum of individual masses of the constituent particles.     

Rough Solutions of Einstein Vacuum Equations in CMCSH Gauge

In this paper, we consider very rough solutions to the Cauchy problem for the Einstein vacuum equations in CMC spatial harmonic gauge, and obtain the local well-posedness result in H ^s , s > 2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric g, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation ${\square_{\bf g} \phi=0}$ directly.     

Periastron shift in Weyl class spacetimes

The periastron position advance for geodesic motion in axially symmetric solutions of the Einstein field equations belonging to the Weyl class of vacuum solutions is investigated. Explicit examples corresponding to either static solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or stationary solutions (single rotating Chazy-Curzon and Kerr black hole) are discussed. The results are then applied to the case of S2-SgrA^* binary system of which the periastron position advance will be soon measured with a great accuracy.     

Scale Transformation,Modified Gravity,and Brans-Dicke Theory

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in f(R) metric formalism nor the ones in f(ℛ) Palatini formalism, whereas the modified source terms are formally equivalent to those of f(R)=\frac12R²f({\mathcal{R}})=\frac{1}{2}{\mathcal{R}}^{2} gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with w = -\frac32\omega=-\frac{3}{2} is explicitly shown, provided the dilaton field is condensated to its vacuum state.     

Higher-dimensional vacuum solutions of Einstein's field equations

Some general solutions of the (general)D-dimensional vacuum Einstein field equations are obtained. The four-dimensional properties of matter are studied by investigating whether the higher-dimensional vacuum field equations reduce (formally) to Einstein's four-dimensional theory with matter. It is found that the solutions obtained give rise to an induced four-dimensional cosmological perfect fluid with a (physically reasonable) linear equation of state.     

Universal temperature corrections to the free energy for the gravitational field

The temperature correction to the free energy of the gravitational field is considered which does not depend on the Planck energy physics. The leading correction may be interpreted in terms of the temperature-dependent effective gravitational constant G_eff. The temperature correction to appears to be valid for all temperatures T?E_Planck. It is universal since it is determined only by the number of fermionic and bosonic fields with masses m?T, does not contain the Planck energy scale E_Planck which determines the gravitational constant at T=0, and does not depend on whether or not the gravitational field obeys the Einstein equations. That is why this universal modification of the free energy for gravitational field can be used to study thermodynamics of quantum systems in condensed matter (such as quantum liquids superfluid ³He and ⁴He), where the effective gravity emerging for fermionic and/or bosonic quasiparticles in the low-energy corner is quite different from the Einstein gravity.